Geodesic
A~recursive algorithm for decoding some subsets of first-order Reed--Muller codes
Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 130-135.

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We give a recursive algorithm for decoding a binary code that is determined as the subset of words of a first-order Reed–Muller code given by linear Boolean functions in $n$ variables of fixed weight $r$ (the number of real variables). We show that the complexity of decoding these subsets of coded words can be estimated by the number $(r+1)\cdot2^n$ of operations of the type of the addition of two numbers, which improves the estimate $(2r+1)\cdot2^n$ already known. This algorithm for the case of decoding the subsets of even [odd] weight $r$ has complexity $n\cdot 2^{n-1}$. 
@article{DM_1992_4_2_a14,
     author = {A. S. Logachev},
     title = {A~recursive algorithm for decoding some subsets of first-order {Reed--Muller} codes},
     journal = {Diskretnaya Matematika},
     pages = {130--135},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_2_a14/}
}
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A. S. Logachev. A~recursive algorithm for decoding some subsets of first-order Reed--Muller codes. Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 130-135. http://geodesic.mathdoc.fr/item/DM_1992_4_2_a14/